In the latest showdown between the two factions fighting for the soul of the GOP, both sides could claim victory in Tuesday's primaries, with tea party candidates winning races in Connecticut and Florida and "establishment" Republicans prevailing elsewhere in Florida and Wisconsin.

But in Connecticut, World Wrestling Entertainment executive Linda McMahon won by a landslide against former longtime congressman Chris Shays, who struggled to hold his own against her formidable challenge, propped up by millions of dollars she poured into her own campaign.

Mr. Shays, who had previously insisted he wouldn't support Mrs. McMahon if she won, did an about-face on Tuesday night, congratulating his opponent and saying he would root for her in November.

Mrs. McMahon, who lost in her bid for the Senate two years ago by 12 points, told supporters her race against Rep. Chris Murphy, who won the Democratic Party's contest, will be all about jobs.

“The issue that will decide this election is who is best able to address the economic crisis that threatens our future and who best understands how to create jobs for the over 150,000 people in Connecticut who wake up every morning without a job,” she said, celebrating her victory at the Hilton Hotel in Stamford.

Each of the three Republican Senate primary winners will go into the fall as underdogs, but party leaders are optimistic about picking off a blue seat. The GOP needs to pick up four Senate seats to seize majority in the upper chamber.

Democrats currently hold the three seats that were in play Tuesday, but the retirement of Sens. Joe Lieberman and Sen. Herb Kohl could crack open the door for Republicans in Connecticut and Wisconsin. In Florida, Mr. Mack is closely trailing Sen. Bill Nelson, who easily won his Democratic Party primary.

Mrs. McMahon, in particular, will face an uphill fight to break up the state's all-Democrat congressional delegation.

Polls over the last few months have shown Mrs. McMahon narrowing her gap behind Mr. Murphy, but she still lagged eight points behind the two-term House member in a recent survey by Public Policy Polling, a Democrat-affiliated firm.

After Mrs. McMahon won the GOP nomination two years ago, using millions of dollars of her personal wealth to spread her name around the state, she lost handily to Sen. Richard Blumenthal on Election Day.

Dramatically overspent by Mrs. McMahon, Mr. Shays had spent the race in his opponent's shadow.

As he touted his own 21-year House career, he tried to use her career spent building up World Wrestling Entertainment to sour voters against her, highlighting controversies over steroid abuse in the industry, its portrayal of women and the mentally handicapped and early deaths of performers and even comparing her to Playboy founder Hugh Hefner.

In Wisconsin, Tommy Thompson holds the electability card, after serving four terms as governor and as Secretary of Health and Human Services under President George W. Bush. A poll earlier this month indicated he was the only one of the four GOP frontrunners who could defeat Democratic nominee Tammy Baldwin among likely voters.

But Mr. Thompson never managed to dominate a crowded GOP field, where he was closely trailed by Mr. Hovde, former Rep. Mark Neumann and state Assembly Speaker Jeff Fitzgerald, who attacked him for supporting a version of President Obama’s health care law as it moved through Congress in 2009.

Tea party candidates have made a strong showing in the Republican primaries so far, with voters choosing Indiana state treasurer Richard Mourdock over Sen. Richard Lugar in Indiana and former Texas Solicitor General Ted Cruz over the state’s Lt. Gov. David Dewhurst.

But establishment Republicans like Mr. Shays were hoping for a win like the one Rep. Todd Akin pulled off last week in Missouri, unexpectedly winning a tight three-way contest and earning the right to compete against Sen. Claire McCaskill in November.

That was no problem for Mr. Mack, who led his closest opponent, Dave Weldon, by 59 to 20 percent. Sen. John Cornyn, chairman of the National Republican Senatorial Committee, congratulated Mr. Mack on his primary victory.

“The difference in this race is abundantly clear. Connie Mack will work with Governor Romney to protect and strengthen Medicare, enact pro-growth policies that will create jobs and finally balance our budget,” said Mr. Cornyn, referring to GOP presidential nominee Mitt Romney.